Abstract:
A magma S that meets the identity, xy ¢z = zy ¢x; 8x; y; z 2 S is called an AG-groupoid. An AG-groupoid S gratifying the paramedial law: uv ¢ wx = xv ¢ wu; 8 u; v; w; x 2 S is called a paramedial AGgroupoid. Every AG-grouoid with a left identity is paramedial. We extend the concept of inverse AG-groupoid [4, 7] to paramedial AG-groupoid and investigate various of its properties. We prove that inverses of elements in an inverse paramedial AG-groupoid are unique. Further, we initiate and investigate the notions of congruences, partial order and compatible partial orders for inverse paramedial AG-groupoid and strengthen this idea further to a completely inverse paramedial AG-groupoid. Furthermore, we introduce and characterize some congruences on completely inverse paramedial AG-groupoids and introduce and characterize the concept of separative and completely separative ordered, normal sub-groupoid, pseudo normal congruence pair, and normal congruence pair for the class of completely inverse paramedial AG-groupoids. We also provide a variety of examples and counterexamples for justification of the produced results.
Page(s):
19-33
DOI:
DOI not available
Published:
Journal: Punjab University Journal of Mathematics, Volume: 53, Issue: 2, Year: 2021
Keywords:
congruences
,
paramedial AGgroupoids
,
Completely inverse AGgroupoids
,
natural partial order